Optimal Purchasing Strategy Research Articles

Research on Resource Allocation of Autonomous Swarm Robots Based on Game Theory

To address the issue of resource allocation optimization in autonomous swarm robots during emergency situations, this paper abstracts the problem as a two-stage extended game. In this game, participants are categorized as either resource-providing robots or resource-consuming robots. The strategies of the resource-providing robots involve resource production and pricing, whereas the strategies of the resource-consuming robots consist of determining the quantity to be purchased based on resource pricing. In the first stage of the game, the resource-providing robots use the Cournot game to determine the resource production according to market supply and demand conditions; in the second stage of the game, the resource-providing robots and the resource-consuming robots play the price game and establish the utility function of the swarm robots to seek the optimal pricing and the optimal purchasing strategy of the swarm robots. After the mathematical derivation, this paper demonstrates the existence of a single Nash equilibrium in the constructed game. Additionally, the inverse distributed iterative search algorithm solves the game’s optimal strategy. Finally, simulation verifies the game model’s validity. This study concludes that the designed game mechanism enables both sides to reach equilibrium and achieve optimal resource allocation.

Strategic interaction of original equipment manufacturers between outsourcing and purchasing in a quality-differentiated market.

Economic globalization has swept the whole world. To focus on their main business, enterprises that are referred to as original equipment manufacturers (OEMs) outsource non-core production activities to contract manufacturers (CMs). By constructing a two-level supply chain consisting of two competing OEMs and one upstream CM, the strategic interaction of the OEMs between outsourcing and purchasing is studied. Specifically, the CM can offer custom- and predefined modes of original equipment manufacturing (namely, CO mode and PO mode, respectively). The former mode enables OEMs to determine product quality, while the latter only allows them to purchase from several quality configurations. The results show that, first, since the CO mode allows the adopter to lead the product design, whether to choose this mode depends on the required R&D cost. Interestingly, however, a lower R&D cost does not necessarily result in the adoption of the CO mode if the product quality difference is small under the PO mode. Second, the optimal purchasing strategy of an OEM is indifferent to the outsourcing mode (CO and PO) of its rival but significantly affected by the quality cost. However, compared to the PO mode, choosing the CO mode would cause the competitor to suffer more profit losses. Third, differing from the prior literature, this paper finds that when the downstream OEM can make quality decisions, although this may lead to profit loss of the contract manufacturer in some channels, it could benefit the CM overall.

Contingent or stable dual sourcing? The preferences of manufacturers and suppliers under supply disruption and competition

ABSTRACT Manufacturers will adopt different strategies to deal with the occurrence of supply disruptions. In this paper, we conduct an analytical game-theoretical study to consider a supply chain with two suppliers (a reliable supplier and an unreliable supplier) and two manufacturers (manufacturers 1 and 2). Manufacturer 2 only orders products from the reliable supplier (Supplier R), while Manufacturer 1 can choose one of the two purchasing strategies: ‘contingent dual sourcing’ or ‘stable dual sourcing’. We study the optimal purchasing strategy of Manufacturer 1 and Supplier R under supply disruptions and competition. We find that Manufacturer 1 prefers the ‘stable dual sourcing’ strategy only if the proportion of order quantity from the unreliable supplier and the potential market size are relatively large, and Supplier R prefers the ‘contingent dual sourcing’ strategy only if the proportion of order quantity from the unreliable supplier is large, the potential market size and disruption probability is not too large.

PURCHASING STRATEGIES IN THE KRALJIC PORTFOLIO MATRIX – A CASE STUDY IN OPEN PIT COAL MINING

Kraljic matrix (or Kraljic model) is a method used to segment the purchases or suppliers of a company by dividing them into four quadrants, based on the complexity (or risk) of the supply market (such as monopoly situations, barriers to entry, technological innovation) and the importance of the purchases or suppliers (determined by the impact that they have on the profitability of the company). This quandrant allows the company to define the optimal purchasing strategies for each of the four types of purchases or suppliers. In coal mining company, hundred thousand goods, part number or SKUs are purchased by corporate in fulfilling its mining operations requirement. However, the commodities generally purchased by open pit coal mining company are classified into 6 (six) classes which are fuel, maintenance of mobile equipment, blasting material, tyre, lubricants, and others. With the complexity of dealing with suppliers, it is mandatory for developing purchasing strategies as part of managing of supply chain. Mining operations and profitability of coal mining company shall depend on the total cost of ownership in purchasing the abovementioned commodities. This Kraljic Portfolio Model (1983) will assist coal mining company in applying purchasing strategies based on the class or quadrant which has been developed. Objective of this research is to develop purchasing strategies by empirically quantifying using data from a comprehensive survey among purchasing professionals in coal mining industry. Kraljic Portfolio Matrix is developed with 2 (two) stages of questioner. First questioner is to assess the importance level of each attribute in the dimension of purchasing activity by using Analytical Hierarchy Process. Second questioner is to assess every commodity’s scoring against each supply attribute. Subsequently, the matrix is developed by using SPSS (Statistical Product and Service Solutions) software. This research successfully classifies purchasing commodity in the appropriate quadrant of Kraljic Portfolio Matrix. By classifying the commodities purchased by coal mining company in the right quadrant of Kraljic Portfolio Matrix, the company will be able to implement the right purchasing strategies which will be different in one quadrant and another.

On Multi-Resource Procurement in Internet Access Markets

With the increasing popularity and significance of content delivery services, especially video streaming, stringent Quality of Service (QoS) requirements have been placed upon Internet content providers (CPs). As a result, CPs have strong incentives to pay for resources such as premium peering bandwidth and cache capacity that ameliorate service quality. In this paper, we study an Internet access market with multiple access resources that CPs can purchase to enhance service quality. We build a detailed content delivery model, through which we characterize the traffic throughput and the resulting utilities of CPs and social welfare. We show that a market equilibrium exists for a multi-resource market, at which the optimization problems for individual utilities and social welfare coincide. Furthermore, we characterize the optimal purchasing strategies of CPs as well as how varying parameters are going to change the market equilibrium via sensitivity analysis.

On multi-resource procurement in internet access markets: Optimal strategies and market equilibrium

With the increasing popularity and significance of content delivery services, especially video streaming, stringent Quality of Service (QoS) requirements have been placed upon Internet content providers (CPs). As a result, CPs have strong incentives to pay for resources such as premium peering bandwidth and cache capacity that ameliorate service quality. In this paper, we study an Internet access market with multiple access resources that CPs can purchase to enhance service quality. We build a detailed content delivery model, through which we characterize the traffic throughput and the resulting utilities of CPs and social welfare. We show that a market equilibrium exists for a multi-resource market, at which the optimization problems for individual utilities and social welfare coincide. Furthermore, we characterize the optimal purchasing strategies of CPs as well as how varying parameters are going to change the market equilibrium via sensitivity analysis.

Estimation of endogenously sampled time series: The case of commodity price speculation in the steel market

We consider the problem of estimating a Markov process that is endogenously sampled. We observe a discrete-time Markov process {pt} at a set of random times {t1,…,tn} that depend on the outcome of a probabilistic sampling rule that depends on the state of the process and other observed covariates xt. We focus on a particular example where pt is the daily wholesale price of a standardized steel product. The endogenous sampling problem arises from the fact that we only observe pt on the days the firm purchases steel. We show how to solve this problem under two different assumptions about firm behavior: (1) optimality: the timing of steel purchases is governed by an optimal purchasing strategy that maximizes expected discounted profits, and (2) potential suboptimality: we allow the firm to use any randomized, Markovian purchasing strategy. In the latter case, the estimation problem becomes semi-parametric and we use the method of sieves to estimate a flexible parametric approximation to the firm’s purchasing behavior that best fits the data without imposing optimality. We show how estimation of this model becomes tractable under either of these assumptions using the method of simulated moments (MSM). We simulate realizations of wholesale steel prices and sample them in the same way as they are sampled in the actual data, i.e. only on days where purchases occur. We use the MSM estimator to estimate a truncated lognormal AR(1) model of the wholesale price processes for particular types of steel plate and test and reject the assumption that the firm is behaving optimally.

Load Aggregator Purchase Optimization Strategy Considering Renewable Energy Quota

The introduction of the renewable energy quota system has an impact on the benefits of all market players in the electricity market. This paper aimed at the decision making of load aggregators’ electricity purchase under the assessment of renewable energy quota. Firstly, the market subject, assessment method and strategy of renewable energy quota system were analyzed effectively. Then the scenario of electricity purchasing faced by load aggregators was described and the optimal decision-making model of electricity purchasing by load aggregators considering renewable energy quota was proposed. At last, the model proposed in this paper was verified by relevant examples, and the results show that the optimal purchasing strategy of load aggregator proposed in this paper had obvious economy.

Optimal Procurement Strategies for a Risk-Averse Buyer When Price Is Uncertain

A procurement model is built based on the expected utility theory when purchase price is uncertain. The optimal purchasing strategy for a risk-averse manufacturer is obtained. And the influence of different factors on the optimal purchasing strategy is analyzed. The results show that the relationship between the optimal purchasing quantity and the degree of risk aversion depends on the relative level of procurement cost at that time. As the price volatility or drift rate increases, the purchase amount in the early stages will increase, and the purchase amount in the later stages will decrease. Finally, it is demonstrated that the procurement strategy of a risk-neutral manufacturer is a bang-bang strategy, which is different from the procurement strategy of a risk-averse manufacturer.

Block Trading: Building up a Stock Position Under a Regime Switching Model

This work is intended to systematically characterize the problem of block trading. The author characterizes it as a constrained optimal purchasing (or control) problem, on behalf of the vendee. The purpose of this work is to investigate the optimal purchasing strategies and give quantitative reference information on the pricing of block trade. Noting that large block of stock trading may result in the price fluctuation and different market environment may lead to distinct investing strategies, the controlled diffusion model with regime switching is adopted, which can be used to represent distinct environment of financial market, and the model is modified to allow the price impact, by allowing the drift depend on the purchase rate. Where the switching regimes can be completely observable or unobservable (hidden). Which is a significant difference in contrast to most market models in the existing literature. The objective is to maximize the total discounted shares of the underlying stock, subject to the expected fund for building up corresponding position with an upper bound. This work mainly focuses on the completely observable case, as to the case with hidden regimes, this work just briefly talk about how to reduce the unobservable model to a completely observable one. In the completely observable case, to solve this constrained control problem, the Lagrange multiplier methods and the dynamic programming approaches are used. Though optimality is obtained, what is still lacking is an explicit solution to the optimality equation. To overcome this difficulty, the two loop approximation scheme is given. For fixed Lagrange multiplier, the inner loop is to obtain optimal strategies, which is based mainly on the finite difference approximation. While, the outer loop is a stochastic recursive approximation algorithm to get the optimal Lagrange multiplier. Convergence results are obtained for both the inner and the outer approximations. The quantitative pricing information is related to the threshold levels of the optimal purchasing strategy. Numerical examples are also provided to illustrate our results. Finally, as to the unobservable case, by using the well known Wonham filter approach, one can reduce the unobservable case to a completely observable one.

A Stackelberg Game Model with Supply Chain Option Contracts under Random Yield and Stochastic Demand

Consider a supply chain consisting of a retailer and a supplier, and the yield of the supplier is random while the market demand of the retailer is stochastic. Due to the double marginalization, the wholesale price contract can’t achieve the coordination of the supply chain, we introduce option contracts into the supply chain in order to investigate whether option contracts can improve the supply chain’s performance under the circumstance where the yield and demand are all uncertain. Through establishing the dynamic Stackelberg game model, which is dominant by the retailer, we discuss the optimal production strategy of the supplier and the optimal purchasing strategy of the retailer, find that the relationship between the production input and the option order quantity is non-linear. In addition, sensitivity analysis indicate that the correlations of decision variables with several parameters. Researches show that option contracts not only offering flexibility for retailer’s purchasing, it can also achieve supply chain coordination under some certain conditions.

Retailer’s Procurement Strategy under Endogenous Supply Stability

In this paper, a dynamic model is presented to study retailer’s procurement strategy when supply stability is endogenously determined. The optimal supply stability as well as the optimal purchasing strategy are characterized with a quadratic cost function. Based on these models, the following findings are brought about. Firstly, when the difficulty level of building supply stability exceeds a certain threshold, it would be more profitable for the retailer to choose a less reliable supplier. Secondly, given that the suppliers can get positive profit, the retailer would choose the one who has the strongest ability to be reliable. Thirdly, the equilibrium supply to the retailer would always meet the demand on the retailing market. Finally, emergency procurement is shown to be an effective way to reduce the risk of supply chain disruptions. To better fit the real situations, an extended model which considers the impact of the stability on costs is further discussed.

Supply Chain Design of Manufacturing Processes with Blending Technologies

Blending technologies play an important role in manufacturing. The design and operation of manufacturing processes using blending technologies represent a special range of manufacturing related logistics because the integrated approach of technological and logistic parameters is very significant. This research proposes an integrated model of supply of manufacturing processes using blending technologies. After a careful literature review, this paper introduces a mathematical model to formulate the problem of supply chain design for blending technologies. The integrated model includes the optimal purchasing strategy depending on the characteristics of components to be mixed in the desired proportion and the costs of supply. The integrated model will be described as a linear programming problem. Numerical results with different datasets demonstrate how the proposed model takes technological and logistic aspects into consideration.

Optimal Purchasing of Deferred Income Annuities When Payout Yields are Mean-Reverting*

We determine the optimal lifecycle purchasing strategy for deferred income annuities (DIAs)—which are distinct from single-premium income annuities (SPIAs)—for an individual who wishes to maximize the expected utility of his/her annuity income at a fixed time in the future. In contrast to the vast portfolio-choice literature for SPIAs, we focus on the stochasticity of the DIA’s payout yield and address concerns that rates are currently “too low” to justify irreversible annuitization. We assume a mean-reverting model for payout yields and show that a risk-neutral consumer who wishes to maximize his/her expected retirement income should wait until yields reach a threshold—which lies above historical averages—and then purchase the DIA in one lump sum. In contrast, a risk-averse consumer who is concerned the payout yield will remain below average for an extended period and worries about losing mortality credits while waiting, should employ a barrier purchasing strategy, as in the portfolio choice problem under transaction costs. We illustrate how this insight is applied in the context of annuitization. In fact, the optimal behavior of a risk-averse consumer resembles an asymmetric dollar-cost averaging strategy, with a portion of the DIA-budget spent even while payout rates are below historical averages. As part of our analysis we offer an easy-to-use asymptotic approximation for the optimal purchasing strategy (threshold) and provide some numerical examples to illustrate the concept.

Fuzzy Multicriteria ABC Supplier Classification in Global Supply Chain

The determination of the optimal purchasing strategy in enterprise that is a part of global supply chain could be performed in two steps. In step one, a classification of potential suppliers is performed in order to determine the optimal portfolio of suppliers. This is delivered by using the fuzzy multicriteria proposed ABC classification method. Uncertainties in relative importance of criteria and their values are described by linguistic expressions. Modelling of linguistic expressions is based on the fuzzy sets theory. In the second step, ranking of optimal portfolio of suppliers is performed by using the modified ELECTRE method. The obtained results represent valuable input for determining the long time purchasing strategy and building partnership with the best suppliers. The developed two-step model is verified on real life data. The obtained results indicate good compliance with the opinions management in this type of industry. It is worth to mention that the proposed model can be easily extended and adopted to the analysis of other issues of management which could be applicable in different research areas.

Optimal combined purchasing strategies for a risk-averse manufacturer under price uncertainty

Purpose: The purpose of our paper is to analyze optimal purchasing strategies when a manufacturer can buy raw materials from a long-term contract supplier and a spot market under spot price uncertainty. Design/methodology/approach: This procurement model can be solved by using dynamic programming. First, we maximize the DM’s utility of the second period, obtaining the optimal contract quantity and spot quantity for the second period. Then, maximize the DM’s utility of both periods, obtaining the optimal purchasing strategy for the first period. We use a numerical method to compare the performance level of a pure spot sourcing strategy with that of a mixed strategy. Findings: Our results show that optimal purchasing strategies vary with the trend of contract prices. If the contract price falls, the total quantity purchased in period 1 will decrease in the degree of risk aversion. If the contract price increases, the total quantity purchased in period 1 will increase in the degree of risk aversion. The relationship between the optimal contract quantity and the degree of risk aversion depends on whether the expected spot price or the contract price is larger in period 2. Finally, we compare the performance levels between a combined strategy and a spot sourcing strategy. It shows that a combined strategy is optimal for a risk-averse buyer. Originality/value: It’s challenging to deal with a two-period procurement problem with risk consideration. We have obtained results of a two-period procurement problem with two sourcing options, namely contract procurement and spot purchases. Our model incorporates the buyer’s risk aversion factor and the change of contract prices, which are not addressed in early studies.

Recycling procurement strategies with variable yield suppliers

This paper addresses a procurement issue facing a polystyrene packaging manufacturer considering its optimal purchasing strategies between two suppliers—one providing virgin material, the other offering recycled material. We model a single-period scenario where each supplier sells product with a known yield distribution at market pricing. The manufacturer must choose whether to sole-source or dual-source, as well as determine how much material to purchase from each supplier to meet deterministic demand. Our results indicate that there is a range of prices from the recycled material supplier where dual-sourcing will lead to higher manufacturer profits compared to sole-sourcing. We show, based on the procurement strategy, the optimal quantities to purchase to maximize manufacturer’s expected profit.

Supply Chain Coordination Based on Revenue-Sharing Contracts under Random Demand

To a two-echelon supply chain system consisting of one manufacturer and one retailer under random demand, the game models about decentralized decision and centralized decision are constructed in which the manufacturer is the leader and the retailer is the follower. The retailer’s optimal purchasing strategies about two conditions above are given and the supply chain expected total profits under unique purchasing strategies of the retailer are compared with. Then the relations of supply chain expected total profit between with applying the revenue-sharing contracts situation and with the centralized decision situation are discussed. And the conditions to realize the supply chain perfect coordinating are defined. Finally, numerical analysis shows that applying the revenue-sharing contract in the decentralized supply chain could not only achieve the maximal overall expected performance but also allow both parties to benefit from it.

The mean-WCVaR based model for LDC's optimal portfolio in multi-energy markets

In a competitive electricity market with highly fluctuated electricity price, local distribution companies (LDCs) need to purchase electric power from several energy markets, such as spot markets, long-term tolling agreements and forward contracts, to maximize profits and minimize risks. Conditional Value-at-Risk (CVaR) can measure risk efficiently, but only one kind of price distribution rule may be considered. In fact, the spot electricity price usually does not follow the normal distribution, and it might be shown as logarithmic normal distribution if there was no enough supply at peak load situation. In this paper, a novel WCVaR method—Weighted Conditional Value-at-Risk—is proposed to measure the purchasing risk of LDC with multiple purchase options, especially when the electricity price follows more than one distribution rules. The Mean–WCVaR model is built as a mathematical programing problem to derive the efficient frontier that indicates the optimal tradeoffs available to LDC between expected revenue and purchasing risk in several energy markets. The existence of optimal solution of proposed WCVaR model is proved mathematically. Simulation results show the efficiency of the proposed model. The proposed model provides a new method for LDC to determine the optimal purchasing strategies considering the risk. Copyright © 2011 John Wiley & Sons, Ltd.

Determination of appropriate price level in installed-capacity market

As one of the most important approaches for ensuring adequate generation capacity, and hence reliability of electricity supply, the capacity-obligation mechanism is employed in some operating electricity markets by imposing such an obligation on all load-serving entities (LSEs). To facilitate the enforcement of the obligation, an installed-capacity market is established for the LSEs and generation companies to trade installed capacity. In the paper, the optimal allocation strategies of generation capacity for generation companies between two electricity markets under different levels of installed-capacity prices, as well as the optimal purchasing strategies of LSEs, are first examined, and on this basis a new framework is developed to determine an appropriate level of generation-installed-capacity price for ensuring generation-capacity adequacy. Finally, the proposed method is illustrated by a numerical example.